Answer:
An applicant must score a minimum of 128
Step-by-step explanation:
To solve this question, we make use of the z-score formula.
Z = (X - mean)/standard deviation
Firstly, let’s list out the parameters from the question. From the question, we can deduce that:
Z = 1.5
X = ?
Mean = 110
Standard deviation =12
1.5= (X-110)/12
18 = X - 110
X = 110 + 18
X = 128
Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
The volume of the solid will be the integral from <em>x</em> = 0 to <em>x</em> = 1 of area A. Since the diameter is given by <em>y</em>, then the radius is <em>y/2</em>. Hence, the volume of the solid is:
Substitute:
Simplify:
Integrate:
![\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B1%7D%7B2%7D%5Cpi%20%5Cleft%5B%5Cfrac%7Bx%5E5%7D%7B20%7D%5CBig%7C_0%5E1%5Cright%5D)
Evaluate:
The volume of the solid is π/40 cubic units.
Answer:
x = 10°
y = 25°
Step-by-step explanation:
3x = 5x - 20 because they are alternate interior angles
subtract 5x from each side of the equation:
-2x = -20
Divide both sides by -2:
x = 10°
The sum of the interior angles of any triangle = 180°
2y + 4Y + (5x - 20) = 180°
combine like terms:
6y + 5x - 20 = 180°
add 20 to each side:
6y + 5x = 200°
substitute for x:
6y + 5(10) = 200°
subtract 50 from each side:
6y = 150°
divide both sides by 6:
y = 25°
Answer:
17/6 miles or 2 5/6 miles
Step-by-step explanation:
The train is 17/2 miles
She ran 1/3 of the way
Multiply 1/3*17/2
1/3*17/2 = 17/6
We can change this to a mixed number
17/6 miles =2 5/6 miles
Answer: √3 + 2√2
Step-by-step explanation: Simplify the expression.
Exact Form:
√3 + 2√2
Decimal Form:
4.56047793 . . .
Hope this helps! :) ~Zane
